Question

Question 3. (10 marks)

1. A family member is thinking about funding his granddaughter’s university education in 8 years when she is expected to enrol at UWI, St. Augustine. He opens a special savings account, where he can receive a lump sum in 8 years. If he is desirous of receiving $60,000 in 8 years when his granddaughter is matriculating, how much would you advise him to deposit in the savings account monthly if annual interest rate is 6%? Show all working.

2. As a prospective car-owner, you have researched the automobile market and you are attracted by two offers. A $250,000 BMW X-series and a Mercedes C-series with two different repayment schedules offered by the respective financiers.

The repayment schedule for the BMW X-series requires a down payment of 10% while the repayment schedule for the Mercedes C-series requires a down payment of 15%. If the repayment is over a period of 10 years at an annual loan rate of 7%, what would be the monthly repayment amount for both schedules? Assume that the monthly repayment starts 1 month after the mortgage contract is signed and the down payment made. Show all calculations.

Answer 1

(a)

Monthly (nominal) interest rate = 6%/12 = 0.5%

Number of months = 12 x 8 = 96

Monthly savings ($) = Future value / F/A(0.5%, 96) = 60,000 / 122.8285**

= 488.49

**F/A(0.5%, 96) = [(1.005)⁹⁶ - 1] / 0.005 = (1.6141 - 1) / 0.005 = 0.6141 / 0.005 = 122.8285

(b)

Monthly (nominal) interest rate = 7%/12 = 0.5833%

Number of month = 12 x 10 = 120

(1) BMW - X Series

Loan amount ($) = 250,000 x (100 - 10)% = 250,000 x 90% = 225,000

Monthly loan repayment ($) = Loan amount / P/A(0.5833%, 120) = 225,000 / 86.1313**

= 2,612.29

(2) Mercedes - C Series

Loan amount ($) = 250,000 x (100 - 15)% = 250,000 x 85% = 212,500

Monthly loan repayment ($) = Loan amount / P/A(0.5833%, 120) = 212,500 / 86.1313**

= 2,467.16

**P/A(0.5833%, 120) = [1 - (1.005833)^-120] / 0.005833 = (1 - 0.4976) / 0.005833 = 0.5024 / 0.005833 = 86.1313